{"paper":{"title":"The effect of nonlocal term on the superlinear Kirchhoff type equations in $\\mathbb{R}^{N}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juntao Sun, Tsung-fang Wu","submitted_at":"2018-12-07T14:29:18Z","abstract_excerpt":"We are concerned with a class of Kirchhoff type equations in $\\mathbb{R}^{N}$ as follows: \\begin{equation*} \\left\\{ \\begin{array}{ll} -M\\left( \\int_{\\mathbb{R}^{N}}|\\nabla u|^{2}dx\\right) \\Delta u+\\lambda V\\left( x\\right) u=f(x,u) & \\text{in }\\mathbb{R}^{N}, \\\\ u\\in H^{1}(\\mathbb{R}^{N}), & \\end{array}% \\right. \\end{equation*}% where $N\\geq 1,$ $\\lambda>0$ is a parameter, $M(t)=am(t)+b$ with $a,b>0$ and $m\\in C(\\mathbb{R}^{+},\\mathbb{R}^{+})$, $V\\in C(\\mathbb{R}^{N},\\mathbb{R}^{+})$ and $f\\in C(\\mathbb{R}^{N}\\times \\mathbb{R}, \\mathbb{R})$ satisfying $\\lim_{|u|\\rightarrow \\infty }f(x,u) /|u|^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03037","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}